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Wasfi Shatanawi Ali Raza Muhammad Shoaib Arif Kamaledin Abodayeh Muhammad Rafiq Mairaj Bibi 《计算机、材料和连续体（英文）》2021,66(2):1121-1137
Nonlinear stochastic modeling plays a significant role in disciplines such as psychology, finance, physical sciences, engineering, econometrics, and biological sciences. Dynamical consistency, positivity, and boundedness are fundamental properties of stochastic modeling. A stochastic coronavirus model is studied with techniques of transition probabilities and parametric perturbation. Well-known explicit methods such as Euler Maruyama, stochastic Euler, and stochastic Runge–Kutta are investigated for the stochastic model. Regrettably, the above essential properties are not restored by existing methods. Hence, there is a need to construct essential properties preserving the computational method. The non-standard approach of finite difference is examined to maintain the above basic features of the stochastic model. The comparison of the results of deterministic and stochastic models is also presented. Our proposed efficient computational method well preserves the essential properties of the model. Comparison and convergence analyses of the method are presented. 相似文献
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Prediction-Correction Scheme for Decoupled Forward Backward Stochastic Differential Equations with Jumps 
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下载免费PDF全文 By introducing a new Gaussian process and a new compensated Poisson random
measure, we propose an explicit prediction-correction scheme for solving decoupled
forward backward stochastic differential equations with jumps (FBSDEJs). For this
scheme, we first theoretically obtain a general error estimate result, which implies that
the scheme is stable. Then using this result, we rigorously prove that the accuracy of
the explicit scheme can be of second order. Finally, we carry out some numerical experiments to verify our theoretical results. 相似文献
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Kamaleldin Abodayeh Ali Raza Muhammad Shoaib Arif Muhammad Rafiq Mairaj Bibi Muhammad Mohsin 《计算机、材料和连续体（英文）》2020,62(3):1125-1142
This paper aims to perform a comparison of deterministic and stochastic models. The stochastic modelling is a more realistic way to study the dynamics of gonorrhoea infection as compared to its corresponding deterministic model. Also, the deterministic solution is itself mean of the stochastic solution of the model. For numerical analysis, first, we developed some explicit stochastic methods, but unfortunately, they do not remain consistent in certain situations. Then we proposed an implicitly driven explicit method for stochastic heavy alcohol epidemic model. The proposed method is independent of the choice of parameters and behaves well in all scenarios. So, some theorems and simulations are presented in support of the article. 相似文献
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Zafar Iqbal Muhammad Aziz-ur Rehman Nauman Ahmed Ali Raza Muhammad Rafiq Ilyas Khan Kottakkaran Sooppy Nisar 《计算机、材料和连续体（英文）》2022,71(2):2141-2157
In this article, a brief biological structure and some basic properties of COVID-19 are described. A classical integer order model is modified and converted into a fractional order model with as order of the fractional derivative. Moreover, a valued structure preserving the numerical design, coined as Grunwald–Letnikov non-standard finite difference scheme, is developed for the fractional COVID-19 model. Taking into account the importance of the positivity and boundedness of the state variables, some productive results have been proved to ensure these essential features. Stability of the model at a corona free and a corona existing equilibrium points is investigated on the basis of Eigen values. The Routh–Hurwitz criterion is applied for the local stability analysis. An appropriate example with fitted and estimated set of parametric values is presented for the simulations. Graphical solutions are displayed for the chosen values of (fractional order of the derivatives). The role of quarantined policy is also determined gradually to highlight its significance and relevancy in controlling infectious diseases. In the end, outcomes of the study are presented. 相似文献
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Muhammad Shoaib Arif Ali Raza Wasfi Shatanawi Muhammad Rafiq Mairaj Bibi 《计算机、材料和连续体（英文）》2019,61(3):1025-1043
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Jinhong Jia Zhiwei Yang Xiangcheng Zheng & Hong Wang 《East Asian journal on applied mathematics.》2022,12(3):673-695
We prove the well-posedness of a nonlinear hidden-memory variable-orderfractional stochastic differential equation driven by a multiplicative white noise, in whichthe hidden-memory type variable order describes the memory of a fractional order. Wethen present a Euler-Maruyama scheme for the proposed model and prove its strongconvergence rate. Numerical experiments are performed to substantiate the theoreticalresults. 相似文献
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复合环境激励下的声振耦合分析 总被引：2，自引：0，他引：2
基于有限元和边界元理论,建立了仪器舱典型结构的耦合模型,分析了声振耦合对结构响应的影响。当典型结构经受随机振动+混响声场复合环境激励时,采用随机分析的原理,用谱分析的分析方法定性的分析结构的动力响应情况,推导了节点响应谱密度的计算公式,解决了Sysnoise软件同时对声振复合环境进行数值模拟的问题。仿真结果表明：声振耦合影响结构的响应,且在各频率上影响程度不同,在低频时较弱,相当于附加阻尼的效果,随着频率的升高,耦合程度随之加强,改变了结构的响应分布;对声振复合环境数值模拟,在低频部分,随机振动激起的响应占主要部分,随着频率的升高,混响声场激起的响应占主要部分,混响声场激起的模态数也要多于随机振动激起来的。 相似文献
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对连续Sylvester矩阵方程的数值算法进行了深入研究,并创新性地提出了一种参数化单步HSS迭代方法.该方法具有独特的求解思路,并证明了其收敛性.为提升性能,通过最小化迭代矩阵谱半径上界寻找拟最优参数.数值实验验证了新方法的有效性和稳健性,展示了其在求解连续Sylvester矩阵方程时的高效和稳定,为相关数值计算提供新工具. 相似文献
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本文利用修正的block-by-block方法针对脉冲微分方程构造了高阶数值格式．修正的block-by-block方法是传统的block-by-block方法的改进,其优点是除第一块外其余每块都能够解耦求解积分方程的高阶数值方法．首先,把脉冲微分方程等价转化为脉冲型积分方程,并利用修正的block-by-block方法进行离散,得到在两个相邻脉冲点中除第一块外其余每块都解耦的高阶数值格式．其次,利用离散的Grownwall不等式证明了数值解逼近精度为四阶．最后,一系列的数值算例验证了理论分析的正确性． 相似文献
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Convergence of Recent Multistep Schemes for a Forward-Backward Stochastic Differential Equation 下载免费PDF全文
下载免费PDF全文 Convergence analysis is presented for recently proposed multistep schemes,
when applied to a special type of forward-backward stochastic differential equations (FBSDEs)
that arises in finance and stochastic control. The corresponding $k$-step scheme admits
a $k$-order convergence rate in time, when the exact solution of the forward stochastic
differential equation (SDE) is given. Our analysis assumes that the terminal conditions
and the FBSDE coefficients are sufficiently regular. 相似文献
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Le Van Hien 《Dynamical Systems: An International Journal》2017,32(2):295-303
In this paper, a periodic SI model with delays is studied. By utilizing the Lyapunov–Krasovskii functional method, a novel explicit criterion for the existence and uniqueness and global asymptotic stability of positive periodic solution is established. Finally, a numerical example is given to illustrate the effectiveness of the obtained results. 相似文献
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随机微分方程广泛地出现于经济学、生物学、物理学、电子、无线电通讯等领域,所以研究随机微分方程的解是十分必要的。由于随机微分方程的解析解求解困难,其数值方法的研究越来越引起人们的重视。对于求解随机微分方程的数值方法,衡量其有效性的标准是收敛性和稳定性。本文证明混合欧拉格式用于求解自治标量随机微分方程时,在方程的偏移系数和扩散系数均满足线性增长条件和全局Lipschitz条件时的收敛性,并且求出了局部均值收敛阶和均方强收敛阶。接着讨论了两种试验方程混合欧拉格式的稳定性。 相似文献
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Debraj Ghosh Roger Ghanem 《International journal for numerical methods in engineering》2008,73(2):162-184
Given their mathematical structure, methods for computational stochastic analysis based on orthogonal approximations and projection schemes are well positioned to draw on developments from deterministic approximation theory. This is demonstrated in the present paper by extending basis enrichment from deterministic analysis to stochastic procedures involving the polynomial chaos decomposition. This enrichment is observed to have a significant effect on the efficiency and performance of these stochastic approximations in the presence of non‐continuous dependence of the solution on the stochastic parameters. In particular, given the polynomial structure of these approximations, the severe degradation in performance observed in the neighbourhood of such discontinuities is effectively mitigated. An enrichment of the polynomial chaos decomposition is proposed in this paper that can capture the behaviour of such non‐smooth functions by integrating a priori knowledge about their behaviour. The proposed enrichment scheme is applied to a random eigenvalue problem where the smoothness of the functional dependence between the random eigenvalues and the random system parameters is controlled by the spacing between the eigenvalues. It is observed that through judicious selection of enrichment functions, the spectrum of such a random system can be more efficiently characterized, even for systems with closely spaced eigenvalues. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
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Stochastic approximation is a common paradigm for many stochastic recursions arising both as algorithms and as models of some
stochastic dynamic phenomena. This article gives an overview of the known results about their asymptotic behaviour, highlights
recent developments such as distributed and multiscale algorithms, and describes existing and potential applications, and
other related issues.
The work of the second author is supported by the DST grant III 5(12)/96-ET. 相似文献